I am presently in Book 2, which is named Al-Baquarah which makes a lot of references to old testament stories of Moses.

Being someone who isn't well read in the old testament, I'm not familiar enough with other versions of these stories to understand the full context of what is going on... i.e. what purpose the text is meant to serve.

There is enough polemic present that I can speculate with some confidence that the words can be used to connect to the tradition of the god of Abraham (that the god of Muhammad, Allah, is the same god is the same god as the god of Abraham) but also to draw fundamental distinctions and achieve a radical departure from Judaism.

Word Origins: Muslim

There is a section in Al-Baqarah 2:[75 -77] where the word "believers" is disambiguated (or indicated as translated) by the word (Muslims) in parentheses. This may indicate an arabic literal from the untranslated original text.

After seeing this, I felt curious and started rooting around the interwebs for original senses of the word "Muslim". To the Bat-Google!